When is tit-for-tat unbeatable?

We characterize the class of symmetric two-player games in which tit-for-tat cannot be beaten even by very sophisticated opponents in a repeated game. It turns out to be the class of exact potential games. More generally, there is a class of simple imitation rules that includes tit-for-tat but also imitate-the-best and imitate-if-better. Every decision rule in this class is essentially unbeatable in exact potential games. Our results apply to many interesting games including all symmetric 2 $$\times $$ 2 games, and standard examples of Cournot duopoly, price competition, public goods games, common pool resource games, and minimum effort coordination games. Copyright Springer-Verlag Berlin Heidelberg 2014